Answer:
B
Explanation:
the sum of all angles in a triangle is always 180°.
the triangle RTQ is an isoceles triangle (both legs and therefore both baseline angles are equal), because we are dealing with a regular polygon.
so the angle RQT is the same as angle TRQ.
angle RQT = (180 - 108)/2 = 72/2 = 36°.
now, the polygon interior angle RQP is the supplementary angle to angle RQT (that means together they represent one side of a line like TP in this case, and therefore 180°).
angle RQP = 180 - 36 = 144°.
we know that the sum of all interior angles in a polygon is
(n - 2)×180
with n being the number of sides.
and each interior angle in a regular polygon is therefore
(n - 2)×180/n
we know that the interior angle is 144°.
so,
144 = (n - 2)×180/n
144n = (n - 2)×180 = 180n - 360
0 = 36n - 360
360 = 36n
n = 10
so, B is the right answer.